An Assessment of the Condition of Distribution Network Equipment Based on Large Data Fuzzy Decision-Making

Abstract

As one of the most important components of power grid, a distribution network is the most vulnerable part in the face of various uncertainties, and influences the stability and economy of a power system. In this paper, the operational information, hardware information and human factors were considered, and a state evaluation model of multi-source information fusion was established. Based on big data fuzzy iteration method and a weighted expert library, a weighted distribution of multi-source information was obtained, and an equipment condition assessment was carried out reasonably. Taking the distribution transformer as an example, the assessment showed that fusion of multi-source information presented in this paper is more comprehensive, and has the ability to reflect the state of equipment. The method proposed in this paper can accurately judge the running state of distribution equipment based on all kinds of information, and provides a reference for the follow-up power marketing for the status assessment of the user equipment.

1. Introduction

With the increasing demand of power and the gradually expanding scale of power grids, higher requirements have been placed on the power supply reliability of systems. In order to improve the reliability of power supply, it is one of the most important tasks to analyze the operational status of a distribution network, and evaluating the status of distribution equipment for the distribution network is an important part of the transmission and distribution of electric energy in a power system [1,2,3]. Testing the distribution transformers, circuit breakers and other power distribution equipment, and evaluating its operating status, can ensure the safety performance of the equipment and the reliability of the distribution network, and it is of great significance to ensure the safe and stable operation of the distribution network and improve the economics of the power supply enterprise.

Due to the wide distribution and large amount of distribution equipment, and the large amount of operational monitoring data without uniform evaluation standards, great difficulties have been brought to the assessment of distribution equipment [4,5,6,7,8,9,10]. As one of the most important pieces of equipment of a distribution network, power transformers have also been paid much attention.

In response to the above problems, domestic and foreign experts have conducted a lot of research, and fuzzy evaluation, artificial intelligence and other methods are widely used in transformer state evaluation [11,12,13,14,15]. Reference [3] presents an evidential reasoning (ER) approach to the transformer condition assessment [3]. The methodology of transferring the transformer condition assessment problem into a multiple-attribute decision-making (MADM) solution under an ER framework is then presented in [3]. Based on the outputs of the ER approach, system operators can obtain an overall evaluation of an observed unit’s condition; also, several units may be ranked in order of severity for system maintenance purposes [3]. In [16] they used artificial neural networks to construct a multi-information fusion model to comprehensively evaluate transformer status. The validity of the method was verified by a case study. Based on the fuzzy theory, references [17,18,19,20] evaluated the operating state of the transformer, and verified the effectiveness of the evaluation method by example. However, no specific standard was given for the selection of the evaluation index. In reference [21], the transformer evaluation index function was established based on the semi-Cauxi distribution, and the transformer state evaluation model of multi-information fusion was established considering the difference of the initial values of the indicators. In reference [22], an adaptive evolutionary limit learning machine algorithm is proposed, which was applied to the transformer state evaluation process, but the selection of transformer evaluation information needs to be optimized. In reference [23], based on the matter-element differential transformation, a transformer hierarchical evaluation model is established. At the same time, the concept of expert validity material element is introduced to make the weight determination more reasonable. In reference [24], based on DGA and SVM, the transformer state is evaluated, and the oil-immersed transformer is taken as an example for verification. Reference [25] introduces a transformer fleet monitoring solution to help the end user to group transformer assets and react accordingly to monitored situations [25]. Reference [26] establishes an index assessing system, considering the main body, the bushing and the accessories components, employs a Cauchy membership function for fuzzy grades division and represents a fuzzy evidence fusion method to handle the fuzzy evidence fusion processes [26]. In reference [27], a new multi-criterion based fuzzy logic model has been proposed to determine the overall health index of transformers. The method relies on the concentrations of individual dissolved gasses, significant diagnostic test results of transformer oil and paper insulation [27]. In reference [28], a novel method for DGA and FRA results unification is proposed, which is based on fuzzy sets application in failures detection and interpretation stages. In reference [29], a fuzzy logic technique for on-line condition diagnostics of transformer oil on the basis of leakage current flows through silica gel of breather and changes the color of silica gel [29].

The above evaluation methods consider the basic parameters of the transformer, operational data and other factors, but the evaluation criteria are greatly influenced by subjective factors, such as the experience of evaluating individuals and experts. Therefore, it is important to determine an evaluation method that is more in line with the actual operating conditions of the power distribution equipment, which can provide assistance for the state assessment of the distribution transformer, and have reference value for the economics of the power supply enterprise and the reliability of the power marketing.

In this paper, based on the large amount of operational information generated during the operation of the distribution network equipment, a state evaluation model of the distribution network equipment integrating multi-source information is established. The model comprehensively considers the critical state quantities of the distribution network equipment, and based on the fuzzy iterative method of big data and the establishment of the weight expert database, weights the multi-source information and reasonably evaluates the equipment status. Finally, taking the distribution transformer as an example, the evaluation results of the fusion of multi-source information proposed in this paper are proved to be more comprehensive. The method proposed in this paper can accurately judge the running status of the power distribution equipment based on various types of information, and provide a reference for the subsequent power marketing evaluation of the user equipment state, which is more instructive.

2. Feature Extraction and Scoring of Key State Quantities of Distribution Equipment

During the operation of the distribution network equipment, a large number of data are generated, including real-time data, historical data, hardware information, environmental conditions, etc. Therefore, appropriate processing is required to extract key state quantities and establish reasonable evaluation criteria.

2.1. Selection of the State Quantity of a Distribution Transformer

The state quantity of a distribution network device can directly or indirectly characterize various conditions during the operation of the equipment, and has guiding significance for the state evaluation of the distribution network equipment. At present, there are uniform standards and clear specifications in technology [30], as shown in

Table 1. Typical state quantity of a distribution transformer.

Component	State Quantity	Reflected State
Winding and bushing	DC resistance	DC resistance exceeds the range.
	Insulation resistance	Insulation resistance is not normal.
	Temperature	The temperature of the joint is abnormal and The temperature rise is abnormal.
	Load rate	Overload.
	Degree of contamination	Severely contaminated or rusted appearance.
	appearance integrity	damaged appearance.
	The temperature of respirator	Exceed the factory defaults.
	Three-phase unbalance rate	Three-phase unbalance rate is not normal.
Tap changer	Performance	Operation is not Normal.
Cooling system	Mechanical properties	Dry change fan vibration is not normal.
	Temperature	Temperature control device is abnormal.
Tank	Ground distance of the bench	The distance to the ground is not enough.
	Sealing	Finishing seal aging.
	Oil level	Oil level is not normal.
	Oil temperature	Oil temperature is abnormal.
Non-electricity protection device	Insulation resistance	Unqualified insulation.
Ground wire	Exterior	Insufficient connection or insufficient depth of grounding body.
Insulation	Grounding resistance	Grounding resistance is abnormal.
	Withstand voltage test	Pressure resistance is unqualified.
Identification	Identification integrity	Equipment identification is vague, incomplete, wrong, etc.

.

It can be seen from Table 1 that the state of the distribution transformer is large, and it is of great significance to reasonably select the state quantity and establish a scientific and comprehensive evaluation system for the state evaluation of the transformer. Since the distribution transformers used by industry and large users are mainly step-down transformers, and most of them are oil-immersed transformers, refer to the standards such as the State Network Distribution Equipment Status Evaluation Guidelines [31], according to the selection of key state quantities. The principle selects and classifies the state quantities of the distribution transformers in Table 1, as shown in

Table 2. Selection and classification of distribution transformer key state quantity.

Classification	Specific Parts	State Quantity
Hardware situation	Sealing means	Sealing ability ${\mu }_1$
	Degree of insulation	Withstand voltage test ${\mu }_2$
	System contamination	Contamination ${\mu }_3$
	Non-electricity protection device	Insulation resistance ${\mu }_{10}$
	Winding and bushing	DC resistance ${\mu }_{11}$
Operational situation	Oil level	Oil level ${\mu }_4$
	Winding and bushing outer temperature	Temperature ${\mu }_5$
	Grounding condition	Grounding down conductor appearance ${\mu }_6$
	Respirator	Respirator status ${\mu }_7$
	Load situation	Load rate ${\mu }_{12}$
	Three-phase load balancing	Three-phase unbalance rate ${\mu }_{13}$
Human factors	Equipment identity	Completeness of identification ${\mu }_8$
	Tap changer	Tap changer performance ${\mu }_9$

.

2.2. Scoring Criteria for Key State Quantities of Distribution Transformers

After the state quantity is selected, it needs to be scored to further evaluate the state of the distribution transformer. According to the unified regulations, the evaluation principles of each state quantity are shown in

Table 3. Grading standard for distribution transformer status.

Serial Number	State Quantity Name	Evaluation Standard Description of Status Quantity Evaluation
1	Withstand voltage test	Whether the withstand voltage test is qualified or not.
2	Winding DC resistance	(1) The difference between the three phases of A, B and C is not more than 2% of the average value; when no neutral point is taken out, the value is 1%; (2) The relationship between the resistance values of the three phases is consistent with the factory.
3	Insulating oil	The degree of pressure resistance.
4	Insulation resistance	Below 20 °C, no less than 300 MΩ; less than 30% change from the previous time.
5	Equipment identification plate appearance	Whether the appearance is normal or not.
6	Sealing performance	Whether there is oil leakage or oil dropping.
7	Oil level	Whether the oil is abnormal.
8	Respirator performance	Whether the respirator is normal.
9	Grounding condition	Ground resistance cannot be greater than a specific value.
10	Oil temperature	Temperature value.
11	Three-phase unbalance rate	Percentage.
12	Load condition	Refer to the rated capacity to determine whether it is overload.
13	Casing contamination	Score according to the degree of contamination.
14	Temperature control system	Whether the temperature control system is normal.
15	Tap changer	Tap changer.
16	Non-electricity protection device	Whether the insulation is Qualified.
17	Environmental temperature and humidity information	Refer to the transformer equipment manual and determine it according to the temperature and humidity standards of the reference manual.
18	Operation hours	Years from the time of commissioning.
19	Family quality defect	Score according to no defects, potential defects, influential defects, and fatal defects.
20	Similar equipment failure rate	Score according to the probability of failure rate
21	Equipment maintenance record	Whether the equipment has ever failed, whether it has been overhauled.

.

It can be seen from Table 3 that the state quantities of the transformer have both qualitative indicators and quantitative indicators of different orders of magnitude and dimensions, so the state quantities need to be normalized before evaluation. The state quantities, including winding DC resistance, oil temperature and other state quantities, which can make the state of the equipment better when become smaller or lower, are treated by Equation (1); the state quantities such as withstand voltage test, insulation resistance and other state quantities, which can make the state of the equipment better when it becomes more powerful and larger, is treated by Equation (2); for state quantities of qualitative measurements (running time, containment performance, etc.), the degree of deterioration is given empirically based on experience.

$${\mu }_{ij}=\{\begin{array}{cc}0& {\mu }_{ij}\le {\mu }_{ij0}\\ \frac{{\mu }_{ij}-{\mu }_{ij0}}{{\mu }_{ij1}-{\mu }_{ij0}}& {\mu }_{ij0}<{\mu }_{ij}\le {\mu }_{ij1}\\ 1& {\mu }_{ij}>{\mu }_{ij1}\end{array}$$

(1)

$${\mu }_{ij}=\{\begin{array}{cc}1& {\mu }_{ij}<{\mu }_{ij1}\\ \frac{{\mu }_{ij0}-{\mu }_{ij}}{{\mu }_{ij0}-{\mu }_{ij1}}& {\mu }_{ij1}\le {\mu }_{ij}<{\mu }_{ij0}\\ 0& {\mu }_{ij}\ge {\mu }_{ij0}\end{array},$$

(2)

where ${\mu }_{ij}\left(i=1,2,\cdots ,9\right)$ is the value of $j$ is determined by the state quantity; $i$ indicates the relative deterioration degree of the state quantity, and the value range is [0,1]; ${\mu }_{ij}$ indicates the observation value; / indicates the ideal value or the factory value; ${\mu }_{ij1}$ indicates the attention value or the warning value. The value of ${\mu }_{ij0}$, ${\mu }_{ij1}$ refers to reference [32,33].

According to the state quantity evaluation criteria given in Table 3, with reference to [32,33], and combined with the experience of a large number of experts and long-term experience, the evaluation set of the key state quantities of the distribution transformer in Table 2 is shown in

Table 4. Evaluation set of distribution transformer key state quantity.

State Quantity	Description	Evaluation Set
		Excellent	Good	General	Malfunction	Serious Failure
Sealing performance ${\mu }_1$	Oil leakage situation ${\mu }_{1,1}$	0.2	0.2	0.3	0.2	0.1
	Oil dripping situation ${\mu }_{1,2}$	0	0	0.1	0.1	0.8
	Oil spilling situation ${\mu }_{1,3}$	0	0	0	0	1
Withstand voltage test ${\mu }_2$	Pressure resistance ${\mu }_{2,1}$	0	0	0	0.1	0.9
Contamination ${\mu }_3$	A small amount of contamination ${\mu }_{3,1}$	0.9	0.1	0	0	0
	More pollution ${\mu }_{3,2}$	0.8	0.1	0.1	0	0
	Obviously damaged rust ${\mu }_{3,3}$	0.1	0.2	0.3	0.3	0.1
	Severely contaminated and blocked ${\mu }_{3,4}$	0	0	0.2	0.5	0.3
Oil level ${\mu }_4$	Oil level gauge indicates abnormality ${\mu }_{4,1}$	0.1	0.2	0.3	0.2	0.2
	Oil level gauge no indication ${\mu }_{4,2}$	0.1	0.1	0.3	0.3	0.2
Temperature ${\mu }_5$	Temperature of connector is too high ${\mu }_{5,1}$	0.1	0.3	0.4	0.2	0
	Rise of temperature is not normal ${\mu }_{5,2}$	0.1	0.2	0.3	0.3	0.1
Grounding down conductor appearance ${\mu }_6$	Lack of connection ${\mu }_{6,1}$	0.1	0.2	0.3	0.3	0.1
	Insufficient depth ${\mu }_{6,2}$	0.2	0.3	0.4	0.1	0
Respirator condition ${\mu }_7$	The respirator is completely discolored by moisture ${\mu }_{7,1}$	0.3	0.3	0.3	0.1	0
	The respirator is completely breathless ${\mu }_{7,2}$	0.3	0.3	0.3	0.1	0
Identification integrity ${\mu }_8$	Lack of identification ${\mu }_{8,1}$	0	0.1	0.2	0.5	0.2
	Wrong identifies or no identifies ${\mu }_{8,2}$	0	0	0.1	0.4	0.5
Tap changer performance ${\mu }_9$	Tap position power indicates abnormal. ${\mu }_{9,1}$	0	0.5	0.5	0	0

.

3. Weight Determination Based on Fuzzy Iteration and Expert Weighted Database

After the key state quantity of the power distribution switch is selected, it is necessary to perform reasonable weight allocation for each state quantity to perform comprehensive evaluation of the state of the distribution network equipment. In this paper, we use the eclectic fuzzy decision-making and multi-level fuzzy comprehensive evaluation model to analyze the previous data of the distribution transformer; continuously update the weight ratio of the evaluation set through the weight inverse operation; reduce the influence of subjective factors brought by the expert review opinions; and improve the data, the reliability of the analysis and ultimately the establishment of a weight expert database.

3.1. Compromising Fuzzy Decision Weight Solving Process

The flow chart of the compromise fuzzy decision [34] is shown in Figure 1. The basic principle is the virtual fuzzy positive ideal and the fuzzy negative ideal. Then, the Euclidean distance method is used to determine the distance between the candidate object and the fuzzy positive and negative ideals, and the membership degree belonging to the fuzzy positive ideal is calculated to determine the selection scheme. The greater the degree of membership, the better the solution and the priority.

The basic solution steps for the compromising fuzzy decision are as follows:

Step 1: The indicator data is transformed into a triangle fuzzy number representation. Let $F(R)$ be the overall fuzzy set on $R$, set $M\in F(R)$. The membership function ${\mu }_M$ of $M$ is expressed as

$${\mu }_M(x)=\{\begin{array}{l}\frac{x-l}{m-l},x\in [l,m]\\ \frac{x-u}{m-u},x\in [m,u]\\ 0,x<l\mathrm{or}x>u\end{array},$$

(3)

where $l\le m\le u$, and $M$ is called a triangular fuzzy number, which is recorded as $M=(l,m,u)=(m_L,m,m_R)$.

According to the Equation (3), the qualitative index, the quantitative index and the weight data in the state quantity are unified into a triangular fuzzy number.

• For the qualitative indicators ${\mu }_i(i=1,2,\cdots ,9)$ in the distribution transformer, they need to be converted into quantitative indicators according to

  Table 5. Triangular fuzzy number ratio method for transforming qualitative index into quantitative index.

  Quantitative Value Attributes	Cost Indicator	Profitability Indicator
  (0,0,1)	Highest	Lowest
  (1,1,2)	Very high	Very low
  (2,3,4)	High	Low
  (4,5,6)	General	General
  (6,7,8)	Low	High
  (7,8,9)	Very low	Very high
  (9,10,10)	Lowest	Highest

  .
• The quantitative index value ${\mu }_i(i=10,11,\cdots ,13)$ for the critical state quantity of the distribution transformer needs to be written in the form of a triangular fuzzy number, as shown in Equation (4).

  $${\mu }_i=\left({\mu }_i,{\mu }_i,{\mu }_i\right).$$

  (4)

  After all the indicators are converted into triangular fuzzy numbers, the fuzzy indicator matrix is obtained and recorded as $F={(f_{ij})}_{m\times n}$.
• The representation of the triangular fuzzy number of the weight vector. For the quantitative indicator, according to Equation (4), the triangular fuzzy number of its weight is expressed as follows:

  $$w=[(w_1,w_1,w_1),(w_2,w_2,w_2),\cdots (w_i,w_i,w_i)].$$

  (5)

  For the weight of qualitative indicators, use the transformation method of Table 5 to convert it into an expression of triangular fuzzy numbers.

Step 2: Normalize $F$. Suppose there are $N$ evaluation objects, and the evaluation index $j(j\in N)$ corresponds to $N$ fuzzy index values in $F$, and is denoted as $x_i=(a_i,b_i,c_i)$, $(i=1,2,\cdots ,N)$. Then, the normalization equation of $x_i$ is as follows:

• When $x_i$ is the fuzzy indicator value corresponding to the cost indicator, the normalization equation is:

  $$y_i=\left(\frac{\min (a_i)}{c_i},\frac{\min (b_i)}{b_i},\frac{\min (c_i)}{a_i}\wedge 1\right).$$

  (6)
• When $x_i$ is the fuzzy indicator value corresponding to the profitability indicator, the normalization equation is:

  $$y_i=\left(\frac{a_i}{\max (c_i)},\frac{b_i}{\max (b_i)},\frac{c_i}{\max (a_i)}\wedge 1\right).$$

  (7)

  The normalized fuzzy indicator matrix is recorded as $R={(y_{ij})}_{m\times n}$.

Step 3: Construct a fuzzy decision matrix D. The fuzzy decision matrix can be obtained by weighting R:

$$D={(r_{ij})}_{m\times n},$$

(8)

where

$$r_{ij}=w\mathsf{\Theta }{y}_{ij}(i=1,2,\cdots ,N,j=1,2,\cdots ,N)$$

(9)

Step 4: Determine the fuzzy positive ideal $M^{+}$ and the fuzzy negative ideal $M^{-}$.

Assume

$$\begin{array}{l}{M}^{+}=(M_1^{+},M_2^{+},\cdots ,M_N^{+})\\ M^{-}=(M_1^{-},M_2^{-},\cdots ,M_N^{-})\end{array}$$

(10)

where $M_j^{+}=\max \{r_{1j},r_{2j},\cdots r_{nj}\}(j=1,2,\cdots ,N)$ and $M_j^{-}=\max \{r_{1j},r_{2j},\cdots r_{mj}\}(j=1,2,\cdots ,N)$ respectively represent the fuzzy maximum and minimum values corresponding to the fuzzy index of column $j$ in the fuzzy decision matrix.

Step 5: Determine the distance $d_i^{+}$, $d_i^{-}$ between the evaluated object $i$ and $M^{+}$, $M^{-}$.

$$d_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^N{(r_{ij}-M_j^{+})}^2}},i=1,2,\cdots ,N.$$

(11)

$$d_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^N{(r_{ij}-M_j^{-})}^2}},i=1,2,\cdots ,N.$$

(12)

Step 6: Fuzzy optimal decision making. Let the evaluation object i be subordinate to the fuzzy positive ideal membership degree as ${\mu }_i$, and then fuzzy optimal decision making. Let ${\mu }_i$ be the membership degree that the evaluation object $i$ subordinate to fuzzy positive ideal; then

$${\mu }_i=\frac{d_i^{-}}{d_i^{+}+d_i^{-}},i=1,2,\cdots ,N.$$

(13)

Obviously $0\le {\mu }_i\le 1$, if $A_i$ is closer to $M^{+}$, the closer ${\mu }_i$ is to 1. The classification results of the membership degree are used to sort the pros and cons of the sample and form a fuzzy expert group commentary set of the multi-level fuzzy comprehensive evaluation model.

3.2. Multi-level Fuzzy Comprehensive Evaluation Model

In order to reduce the influence of subjective factors caused by expert experience and avoid errors caused by data redundancy or errors or omissions, this paper adopts a combination of eclectic fuzzy decision-making and multi-level fuzzy comprehensive evaluation to improve the evaluation accuracy of distribution transformer state assessment. The specific steps of the model are as follows:

Step 1: Determine the set of objects to be evaluated $X\{x_1,x_2,x_3,\cdots ,x_k\}$; determining factor set $U=\{u_1,u_2,\cdots ,u_n\}$; confirm the comment set $V=\{v_1,v_2,\cdots ,v_n\}$.

Step 2: According to the factor set $U$ and the comment set $V$, the evaluation matrix $R_i$ is obtained.

$$R_i=\{\begin{array}{cccc}{r}_{11}^{(i)}& r_{12}^{(i)}& \cdots & r_{1m}^{(i)}\\ ⋮& ⋮& & ⋮\\ r_{n_{i}1}^{(i)}& r_{n_{i}1}^{(i)}& \cdots & r_{n_{i}m}^{(i)}\end{array}\}.$$

(14)

Step 3: Make a comprehensive decision for each $U_i$. Let the weight of $U_i$ be assigned as $A_i=\left(a_1^{(i)},a_2^{(i)},\cdots ,a_{n_i}^{(i)}\right)$, and ${\displaystyle \sum _{i=1}^{n_i}{a}_i^{(i)}}=1$. If $R_i$ is a one-factor matrix, then the first-level evaluation vector is obtained as follows

$$A_i\times R_i=\left(b_{i1},b_{i2},\cdots ,b_{in}\right)\Delta B_i, i=1,2,\cdots ,s.$$

(15)

Step 4: Think of each $U_i$ as a factor, so $U$ is a single factor set, and the single factor judgment matrix of $U$ is:

$$R=\left(\begin{array}{c}{B}_1\\ B_2\\ ⋮\\ B_s\end{array}\right)=\left(\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1m}\\ ⋮& ⋮& & ⋮\\ b_{s1}& b_{s2}& \cdots & b_{sm}\end{array}\right).$$

(16)

Each $U_i$ is considered part of $U$, reflecting a certain attribute of $U$, which can be weighted according to their importance.

$$A=\left(a_1,a_2,\cdots ,a_s\right).$$

(17)

The second-level fuzzy comprehensive evaluation model is obtained as follows:

$$B=A\times R=\left(b_1,b_2,\cdots ,b_m\right).$$

(18)

If there are more factors in each sub-factor $U_i=\left(i=1,2,\cdots ,s\right)$ you can continue to divide $U_i$.

Step 5: After obtaining the weight distribution, replace it with Step 3 in the basic solution step of the compromise fuzzy decision, that is, the establishment of the fuzzy weight, and then obtain the final computer expert library through repeated iterations. This not only gives a review of the computer expert library for the new data, but also expands the sample data for the computer expert library.

4. Case Analysis

This paper selects 16 distribution transformer data in a certain area to verify the proposed state assessment model.

4.1. Distribution Transformer Basic Parameters

According to Table 2, there are 13 key state quantities of distribution transformers, including four quantitative indicators and nine qualitative indicators. To reduce data redundancy and clearly show the accuracy of the algorithm,

Table 6. The original data of distribution transformer.

Distribution Number	$\mathbf{Score}\mathbf{of}\mathbf{DC}\mathbf{Resistance}{\mathit{\mu }}_{11}$	Expert group’s Fuzzy Score on State Quantity
		$\mathbf{Sealing}\mathbf{Performance}{\mathit{\mu }}_1$	$\mathbf{Insulation}\mathbf{Performance}{\mathit{\mu }}_2$	$\mathbf{Grounding}\mathbf{Condition}{\mathit{\mu }}_6$	$\mathbf{Identification}\mathbf{Situation}{\mathit{\mu }}_8$
$T_1$	97	Excellent	Excellent	Good	Excellent
$T_2$	96	Excellent	Good	Excellent	Good
$T_3$	95	Good	Excellent	Qualified	Good
$T_4$	95	Excellent	Good	Failed	Good
$T_5$	94	Good	Excellent	Good	Failed
$T_6$	93	Excellent	Good	Failed	Good
$T_7$	93	Good	Excellent	Qualified	Qualified
$T_8$	93	Good	Excellent	Good	Qualified
$T_9$	92	Good	Good	Excellent	Qualified
$T_{10}$	92	Failed	Good	Qualified	Excellent
$T_{11}$	92	Failed	Qualified	Good	Excellent
$T_{12}$	91	Good	Good	Qualified	Excellent
$T_{13}$	90	Good	Qualified	Failed	Good
$T_{14}$	89	Qualified	Good	Good	Qualified
$T_{15}$	88	Good	Excellent	Failed	Good
$T_{16}$	86	Good	Qualified	Good	Qualified

shows the rating of the five major factor sets of the distribution transformer, including a quantitative indicator: winding DC resistance; and four qualitative indicators: sealing performance ${\mu }_1$, insulation performance ${\mu }_2$, grounding situation ${\mu }_6$ and marking situation ${\mu }_8$.

4.2. Status Assessment of Distribution Transformers

According to the basic principle of the compromised fuzzy decision, the qualitative indicators (excellent, good, qualified, unqualified) are firstly analyzed according to the quantitative indicators. The quantitative criteria are shown in

Table 7. Quantitative standard for qualitative index of distribution transformers.

Grade	Excellent	Good	Qualified	Failed
Quantization fuzzy number	(85,90,100)	(75,80,85)	(60,70,75)	(50,55,60)

.

The initial triangle weight value is:

$$W={\left[\begin{array}{c}(0.5,0.5,0.5)\\ (0.2,0.2,0.2)\\ (0.15,0.15,0.15)\\ (0.1,0.1,0.1)\\ (0.05,0.05,0.05)\end{array}\right]}^{T}i.$$

The index information and the weight information are transformed into triangular fuzzy numbers, and the fuzzy index matrix F is obtained as follows.

$$F=\left(\begin{array}{ccccc}(96,96,96)& \left(85,90,100\right)& (85,90,100)& (75,80,85)& (75,80,85)\\ (95,95,95)& (85,90,100)& (75,80,85)& (85,90,100)& (65,70,75)\\ (95,95,95)& (70,80,85)& (85,90,100)& (50,60,65)& (65,70,75)\\ (94,94,94)& (85,90,100)& (75,80,85)& (75,80,85)& (75,80,85)\\ (93,93,93)& (75,80,85)& \left(85,90,100\right)& (75,80,85)& (65,70,75)\\ (93,93,93)& (75,80,85)& (50,60,65)& \left(85,90,100\right)& (75,80,85)\\ (92,92,92)& \left(85,90,100\right)& (75,80,85)& (65,70,75)& (75,80,85)\\ (92,92,92)& (75,80,85)& \left(85,90,100\right)& \left(85,90,100\right)& (65,70,75)\\ (92,92,92)& (75,80,85)& (75,80,85)& \left(85,90,100\right)& (75,80,85)\\ (92,92,92)& (50,60,65)& (75,80,85)& \left(85,90,100\right)& (65,70,75)\\ (91,91,91)& (50,60,65)& (65,70,75)& (75,80,85)& \left(85,90,100\right)\\ (90,90,90)& \left(85,90,100\right)& (75,80,85)& (65,70,75)& \left(85,90,100\right)\\ (89,89,89)& (75,80,85)& (65,70,75)& (50,60,65)& \left(85,90,100\right)\\ (89,89,89)& (50,60,65)& (75,80,85)& \left(85,90,100\right)& (75,80,85)\\ (88,88,88)& \left(85,90,100\right)& (75,80,85)& (65,70,75)& (75,80,85)\\ (87,87,87)& (75,80,85)& \left(85,90,100\right)& (75,80,85)& (65,70,75)\end{array}\right).$$

The data in $F$ is normalized to obtain the fuzzy decision matrix $D$. According to Equation (10), the fuzzy positive ideal $M^{+}$ and the fuzzy negative ideal $M^{-}$ are obtained as:

$$M^{+}={\left[\begin{array}{c}(0.5,0.5,0.5)\\ (0.17,0.20,0.20)\\ (0.1275,0.15,0.15)\\ (0.085,0.1,0.1)\\ (0.0425,0.05,0.05)\end{array}\right]}^T M^{-}={\left[\begin{array}{c}(0.4531,0.4531,0.4531)\\ (0.1,0.1222,0.1412)\\ (0.0750,0.0917,0.1059)\\ (0.05,0.0611,0.0706)\\ (0.03,0.0389,0.0441)\end{array}\right]}^T.$$

The fuzzy double peak value and the membership percentage value obtained by the fuzzy optimization decision after multiple times of the cycle are shown in

Table 8. Results of distribution transformer status assessment.

Distribution Number	Fuzzy Positive Ideal	Fuzzy Negative Ideal	Final Score
$T_1$	0.0167	0.1775	91.39
$T_2$	0.03	0.1683	84.88
$T_3$	0.0699	0.1495	82.86
$T_4$	0.0333	0.1608	76.27
$T_5$	0.0465	0.1495	75.08
$T_6$	0.0989	0.1253	72.88
$T_7$	0.0558	0.1495	72.8
$T_8$	0.0501	0.151	68.13
$T_9$	0.0525	0.141	68.03
$T_{10}$	0.1286	0.1036	63.01
$T_{11}$	0.1396	0.0737	60.87
$T_{12}$	0.0685	0.1457	55.88
$T_{13}$	0.1064	0.106	49.92
$T_{14}$	0.1377	0.0956	44.62
$T_{15}$	0.0838	0.1428	40.98
$T_{16}$	0.0896	0.1393	34.54

, and finally, the state evaluation value of the distribution transformer is obtained.

The fuzzy positive ideal and the fuzzy negative ideal are determined by analyzing a large number of transformers of the same type. This paper adopts a combination of eclectic fuzzy decision-making and multilevel fuzzy comprehensive evaluation, and the weights of quantitative indicators and qualitative indicators can be obtained by performing repeated fuzzy iterations. The weight ratio of the evaluation set is constantly updated through the weight inverse operation, reducing the influence of subjective factors brought by the expert review opinions and avoiding errors caused by data redundancy or errors or omissions, which improving the reliability of data analysis and promoting the establishment of the weight expert database, finally. The distances between the evaluated object and the fuzzy positive and negative ideals are determined, and the membership degree belonging to the fuzzy positive ideal is calculated. The greater the membership degree, the better the state of the transformer. The smaller the membership degree, the worse the state of the transformer, so it is necessary for the operation and maintenance personnel to pay attention to it and arrange the maintenance work in good time. The comparison and analysis of the relevant data in Table 6 and Table 8 show that the final score of each transformer in Table 8 can truly reflect the actual operation status of the transformer in Table 6, which provides quantitative parameters for the evaluation of distribution equipment, and which is beneficial to the further focus and field evaluation of the equipment, providing help for maintenance and operation.

The analysis of practical examples shows that the evaluation method is concise and intuitionistic, and the evaluation conclusion not only reflects the state of a single transformer, but also facilitates the ranking of the overall state of the transformer, which provides reasonable suggestions for orderly arrangement of transformer maintenance.

5. Conclusions

Taking the distribution transformer as an example, this paper establishes a self-assessment model of the distribution equipment based on multi-source heterogeneous information fusion. The operation conditions and reliability assessment of the equipment can be obtained through the integration of data from a variety of sources, and maintenance is arranged according to the health state of the equipment, which can support the improvement of power supply reliability and the economy of power marketing.

This method reduces the influence of subjective factors brought by the expert review opinions; avoids errors caused by data redundancy or errors or omissions; and improves the reliability of data analysis and the accuracy of distribution equipment state assessment. The data of 16 distribution transformers in a certain area were selected, their status was evaluated. The effectiveness of the method was verified by a practical example.